I need Smartphone access to WiFi where there is no WiFi

I have an office with a wireless router in one corner of a fairly large house. Internet access is DSL. My computer connects directly to the router with an ethernet cable and does not run on a wireless signal. I have a Cat 5e cable that runs from that router to the opposite corner of the house where my wife's office is. Her computer connects directly to the ethernet cable for internet access (as mine does). There is no wireless reception on her side of the house, mainly because there are about 5 walls and 75 feet between the two offices. The wireless signal only reaches about halfway there. She will be getting a Smartphone soon that she would like to use with a wireless signal for internet access on the phone. What would be the best way to get a wireless signal in her office?

you need a wireless access point. Connect it on the end of the long run of Cat5e in your wife's office. Depending on capabilities of the PC's, you could go 100% wireless by dropping PCi wireless cards into them.

Alternatively you can still use wired to the PC's in that office by using a wireless router rather than a specific access point . Most wireless routers have multiple Ethernet ports too (to connect the PC's) and can act as a wireless access point for the smartphone if correctly configured. You can replicate this by using an Ethernet switch with a simple wireless access point off one leg for the Smartphone and the PC's on the others.

As pointed out by Tinto Tech, a second wireless router (configured as a bridge or access point) will do the trick. If you are a networking newbie, your best bet is to purchase the same brand as your first wireless router -- although different brands do work together, there may be slight inconsistencies in the setup menus that can make you doubt yourself. It's great when you can go back to the first and see what settings are where.

That said, my main wireless router is a Netgear way in the back of the house and I have an additional Apple Airport Express in the living room.